Seven chapters of experiments, and not one of them has answered the only question a newcomer actually asks: what is the electron doing between the slits and the screen? That is not an oversight. The mathematics that predicted every pattern on this site (flawlessly, for a century) is silent on the question, and the experiments cannot break the tie, because the major interpretations of quantum mechanics agree on every number the double slit can produce. They differ in the story: what the wavefunction is, whether anything collapses, what a particle is doing when nobody asks. Same maths, different stories. And every story has a catch.
The wavefunction ψ is a tool for computing probabilities, not a thing in the world. Between source and screen there is no fact about which slit; the question is meaningless until an apparatus makes it answerable. On measurement, ψ collapses: chapter 3's dot is the collapse happening. The eraser holds no mystery: probabilities were always conditional on the whole arrangement, and rearranging the apparatus rearranges the probabilities.
The catch: the theory never says what actually counts as a "measurement". Where exactly does the quantum world hand over to the everyday world? Copenhagen shrugs. It works brilliantly, but it shrugs. This is the measurement problem.
Everett, 1957: there is no collapse; the Schrödinger equation is always true for everything. The electron goes through both slits, and when it meets the screen the electron-plus-screen (and shortly you) enter a superposition: one branch for every dot position. The dot you see marks which branch you are in, nothing more. Which-path detection kills fringes because branches that carry different records can no longer interfere. Chapter 7's decoherence is the branching made irreversible in practice.
The catch: an unimaginable number of parallel worlds, and a genuine puzzle about what "probability" even means when every outcome happens somewhere.
There is always a particle with a definite position, and it rides a real wave. The particle goes through one slit; the wave goes through both, and its interference steers the particle by the guidance equation into the bright channels. Chapter 3's randomness is ignorance, not law: the landing point was fixed by the particle's unknowable starting position. Below: actual trajectories, integrated live from the guidance equation. No cartoon.
Each green thread is one particle's real path through the two-Gaussian-slit wave (the standard Philippidis–Dewdney–Hiley construction, ħ = m = 1). Start positions are drawn from |ψ|²; the blue field is the wave's intensity. Watch what the fan does: trajectories bend where the wave interferes, never cross and pile up in the fringe channels.
The catch: the guidance wave is openly nonlocal: what happens to the particle here can depend instantly on things far away. That sits awkwardly with relativity, which says there is no universal "now".
Strictly a formulation, not an interpretation. But it is the deepest way to see the fringes. The rule: the electron takes every path. Each path contributes a little arrow of the same length, rotated by its action; the amplitude at a screen point is the sum of all the arrows, and probability is the resultant's length squared. Slide the detector across the screen and watch the arrows curl:
Left: a fan of sampled paths through both slits to the detector (drawn at ripple-tank scale so the phases stay legible; the engine is the same at any scale). Each path is coloured by its arrow's angle. Right: those arrows chained tip to tail: the famous curling sum. Bright fringe: the arrows march nearly straight. Dark fringe: they curl into a closed loop and cancel.
The catch: mathematically, none. It is exactly equivalent to the Schrödinger equation. But as a story it inherits the same open question: the arrows are amplitudes, and why the squared result is a probability is exactly what the interpretations above are arguing about. One thing falls out beautifully, though: for heavy objects only the paths near the path of least action add up. Newton's mechanics is the surviving arrow.
Objective collapse (GRW/CSL). Perhaps collapse is physics: every particle spontaneously localises at a tiny random rate, and the rate scales with mass, so electrons wave for eons while cricket balls localise instantly. Unique on this page: it predicts something different, and chapter 7's giant-molecule experiments are steadily narrowing down where it could still hide.
Relational QM & QBism. The wavefunction is not the world but a perspective on it: facts are relative to an observer (relational QM) or ψ is an agent's personal betting book (QBism). The eraser's "paradox" dissolves entirely: updating a betting book rewrites nothing but the book. The catch: many physicists want physics to describe the world, not somebody's notes about it.
| ch. 3's dot | which slit? | the catch | |
|---|---|---|---|
| Copenhagen | collapse | meaningless unasked | what counts as measuring? |
| Many-Worlds | your branch | both, in branches | endless worlds; why odds? |
| de Broglie–Bohm | where it always was | one, definitely | instant action at a distance |
| GRW collapse | real physical event | both, until a hit | new constants, but testable |
Watch the trajectory fan: every thread passes through a single slit and never crosses the midline. Yet the ensemble still lands in fringes. Fringes do not require "both slits" of the particle; they require it of the wave.
How that can workEvery experiment on this site comes out identically in Copenhagen, Many-Worlds and Bohm. That is a theorem, not a coincidence. Only objective collapse dares to differ, which is why chapter 7's molecules matter.
Why experiment can't refereeA collapse nobody can explain, more worlds than you can count, faster-than-light guidance or new constants nobody has confirmed. You have to pick one. Physicists just disagree about which catch annoys them least. That is the whole debate.
Choosing honestly